One Sample t-test
When would you run a One Sample t-test. Or rather, what does a One Sample t-test compare?
- it compares the means between the sample and population
- run a One Sample t-test when the population mean is a known value and the population SD is an unknown value
What is the other name for an Independent Samples t-test
Between-subjects t-test
What is the other name of a Dependent Samples t-test?
Within-groups t-test
Paired Samples t-test
Why would you run a One-way ANOVA instead of just running multiple t-tests?
Reduces Type I Error
Type 1 Error = 1-(1 - α)^C
Why is effect size important?
Using your t-table, if I was running a one tail One Sample t-test with an alpha level of 0.05, and degrees of freedom of 11. Then what is my t-statistic?
1.796
What is one of the two main assumptions for an Independent t-tests?
1. Assumption of normality
2. Assumption of homoscedasticity (variance between the compared groups are approx. equal)
What is the main assumption for dependent t-tests?
Assumption of Normality
How much Type I Error could I potentially have for an alpha level of 0.05 after running 15 t-tests?
Type I Error = 1-(1 - α)^C
Type I Error = 0.5367
Imagine you were studying the effect of stress on heart rate. One group was told to solve simple addition problems while another was told to solve advanced calculus problems, with both groups having their heart rate measured afterwards.
Which test would you run to compare the mean heart rate of these groups?
Independent t-test
When using a One Sample t-test in JASP, it will ask you to select either Student, Wilcoxon or Z Test. Assuming you do not violate any assumptions, and are running a normal One Sample t-test which would you select?
Student
If you happen to fail the assumptions of normality OR equal variance for an independent t-test, then what test should you run.
Violate equal variance = Welch
Violate normality = Mann Whitney U
If you violate the assumption of normality for a dependent t-test, then what test should you run?
Wilcoxon Test
How do you interpret effect size for ANOVAs?
For instance, if η2 = 0.8601, then what would that mean?
86.01% of the variance in the dependent variable can be explained by the independent variable
What are degrees of freedom? Why are they important?
They are the points that are "allowed to vary"
- ie trying to find the mean when you only know 4 of 5 data points
- higher df, the closer it resembles the distribution at times
- also important for reading the t table
- influenced by the number of distinct samples (ie indep. t-test is typc. df-2 vs dep. t-test is typc. df-1)
I am studying Lyme Disease and I want to see if a person's perceived level of sickness (0-30) is related to having the typical "bulls-eye" symptom. I want to compare national rates to the state of PA. I found that the average is μ = 7 on a national level, and that on the state level with a sample of 120 the average was M = 15 (SD = 3).
Run a one tail One-sample t-test with an alpha level of 0.05. Is this sample significantly different from the population?
A one-sample t-test revealed that
the state perceived level of illness for a bulls-eye rash with Lyme Diseases (M = 15
3.30, SD = 3) was significantly different
from the national average (μ =
7), t (119) = 29.21, p < 0.05, Cohen’s d =
2.67.
I am studying the number of wingbeats that ruby-throated hummingbirds can flap their wings in a minute, and I want to see if ruby-throated hummingbirds flap their wings more in high elevation versus low elevation. Hummingbirds in a higher elevation (n = 25) beat there wings on an average of 650 times (SD = 12). While hummingbirds in a lower elevation (n = 23) beat their wings on an average of 890 times (SD = 15).
Run a full one-tail independent t-test with an alpha level of 0.05 to determine if there is a significant difference between these groups.
An independent t-test revealed that hummingbirds in lower elevations more frequently flap their wings (M = 890, SD = 15) in comparison to hummingbirds in higher elevations (M = 650, SD = 12), t (46) = -61.62, p < .05, d = -17.75.
The only assumption listed is the assumption of normality. Why are we no longer worried about equal variance?
Our sample is the same sample
What are post-hoc tests?
Post-Hoc tests look at all possible
combination of groups and tells us which
groups are different from each other using
(corrected) t-tests.
What is the difference between a z-test and a t-test?
- a z-test requires you to know the population mean and SD; a t-test you only know the population mean
- both are a comparison of means, however t-tests can be a comparison of means between samples as well as population; z-test is only comparison of a sample to the population
- assumptions are slightly different; ie z-test uses normal distribution while t-test uses Students t-distribution;
- need to know degrees of freedom for a t-test; other equation differences like with SE, etc.
When running a One Sample t-test in JASP, what number should be placed into the "Test Value" box?
The population mean
How would you go about finding a distribution of differences between means?
Step 1: Randomly take a random sample of N
scores from the population and calculate the
mean
Step 2: Randomly take a random sample of N
scores from the population and calculate the
mean
Step 3: Subtract the second mean from the first
Step 4: Repeat several times
Step 5: Draw a distribution of the mean
differences
Imagine that I am interested in studying social behaviors in cats and I measure the number of times the cats (n = 6) slow blink when presented with a dog when initially presented the the new dog, and a week later when presented again with that dog.
The difference scores between the first time and second time are as listed: 7, 9, 8, 10, 3, and 19. Run a two tail dependent t-test with an alpha level of 0.05.
I retain the null hypothesis that there is no difference in social behaviors between the first interaction with a dog and one week after.
A dependent t-test revealed that cats did significantly blink when re-exposed to a dog (MD = 9.33, SDD = 5.32), t (5) = 4.30, p < .05, d = 1.75.
What is the equation for the degrees of freedom for within groups and between groups for a one-way between subjects ANOVA.
Within Groups: N - k
Between Groups: k - 1
N = sample size of all groups combined
k = number of groups
Imagine that I am interested in measuring stress with from cortisol levels in comparison between two separate groups where one is given simple math problems and another group given advanced calculus problems.
What is the Independent variable, the levels of that variable, and is this a between-subjects or within-subjects design?
IV: stressor
Levels: Simple math, advanced calculus
Between-subjects